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– Raphael♦Dec 3 '18 at 17:03

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$\begingroup$Also, one has to wonder if you've done any research on your own. Even Wikipedia has more examples! There are probably hundreds of examples in the literature.$\endgroup$
– Raphael♦Dec 3 '18 at 17:04

As Raphael commented, there are probably hundreds of examples in the literature. Here are a few simple or notable ones.

Quickselect as mentioned by Yuval's comment. This includes median of the medians algorithm as its special case. This double recursive algorithm is probably more subtle and ingenious then you might have thought. Yuval has also devised an divide-and-conquer algorithm to solve a recent question on how to find a pair of near numbers.

Maximum single-sell profit. Here divide-and-conquer is beaten by dynamic programming, as what happens to the previous problem of maximum subarray.

We can also relate many structural decomposition techniques to divide and conquer. Whenever we are using the recursive nature of a tree graph, it could be considered an application of divide and conquer. Whenever we are using the Jordan blocks of a matrix, it could be considered likewise. When you reduce a problem about a graph to each of its connected component, it could be considered likewise. In this sense, divide-and-conquer appears even more pervasive.

There are also many examples that are better classified as decrease and conquer. Some notables of them are binary search, exponentiation by squaring, Johnson–Trotter algorithm that lists all permutations. Whether we or you would like to consider them as divide-and-conquer (proper) is up to our or your preferences. If you do, it may "help you conceptualize the algorithms that you learn in the course. If you don't find this helpful, just ignore it", says Yuval.

If you have plenty of time to kill, you may enjoy the following tedious exercise.